Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

Advances in Nonlinear Analysis

article

Jagmohan Tyagi¹ 

[1] Indian Institute of Technology Gandhinagar, Vishwakarma Government Engineering College Complex

关键词: Singular elliptic equations;    variational methods;    nontrivial solutions;   

DOI  :  10.1515/anona-2013-0027

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Abstract. In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem -Δℍnu=μg(ξ)u(|z|4+t2)12+λf(ξ,u)$-\Delta _{{\mathbb {H}}^{n}} u= \mu \frac{g(\xi ) u}{(|z|^{4}+ t^{2} )^{\frac{1}{2} }} +\lambda f(\xi , u)$ in Ω, u=0$ u =0$ on ∂Ω$\partial \Omega $ on the Heisenberg group. We employ Bonanno's three critical point theorem to obtain the existence of weak solutions.

【 授权许可】

CC BY